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Scientific Calculator Functions and Formulas

Review scientific calculator formulas for precedence, exponents, roots, logarithms, trigonometry, inverse functions, factorials, percentages, and notation.

How do the Scientific Calculator formulas work?

This formula page defines the variables used by the Scientific Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

A scientific calculator combines numerical constants, unary functions, postfix operations, powers, roots, and binary arithmetic in one expression. Parentheses make the intended structure explicit.

The engine calculates real-number results with finite floating-point arithmetic. It is not a computer algebra system and does not simplify variables or retain arbitrary precision.

Order of Operations

grouping and functions→powers and roots→multiplication and division→addition and subtraction\text{grouping and functions}\rightarrow\text{powers and roots}\rightarrow\text{multiplication and division}\rightarrow\text{addition and subtraction}

Operations at the same addition or multiplication level are evaluated from left to right. Exponents are evaluated from right to left, so 2 raised to 3 raised to 2 is interpreted as 2 raised to the power of 9.

Powers and Roots

xn=x×x×⋯×x⏟n factors,xn=x1/nx^n=\underbrace{x\times x\times\cdots\times x}_{n\text{ factors}},\qquad \sqrt[n]{x}=x^{1/n}

Squaring and cubing are special cases of exponentiation. A root reverses a power when the selected values remain in the real-number domain.

For an even root, a negative radicand has no real result. The reciprocal key uses x raised to -1, which equals 1 divided by x when x is not zero.

Logarithms and Exponentials

log⁡b(x)=y  ⟺  by=x,ln⁡(x)=log⁡e(x),eln⁡(x)=x\log_b(x)=y\iff b^y=x,\qquad \ln(x)=\log_e(x),\qquad e^{\ln(x)}=x

For a real logarithm, x must be positive and the base must be positive and not equal to 1. This calculator provides log base 10 and the natural logarithm base e.

Trigonometric Functions

sin⁡(θ),cos⁡(θ),tan⁡(θ)=sin⁡(θ)cos⁡(θ)\sin(\theta),\qquad\cos(\theta),\qquad\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}

Sine, cosine, and tangent use the selected angle mode. Tangent is undefined wherever cosine is zero, including odd multiples of 90 degrees.

Inverse functions return an angle. Inverse sine and inverse cosine accept real inputs only from -1 through 1.

Degree and Radian Conversion

θrad=θdegπ180,θdeg=θrad180π\theta_{rad}=\theta_{deg}\frac{\pi}{180},\qquad \theta_{deg}=\theta_{rad}\frac{180}{\pi}

A full rotation is 360 degrees or 2 pi radians. Converting the input before evaluating a trigonometric function produces the same mathematical value as selecting the matching angle mode.

Factorial, Percent, and Reciprocal

n!=n(n−1)(n−2)⋯2⋅1,0!=1,p%=p100,x−1=1xn!=n(n-1)(n-2)\cdots2\cdot1,\quad0!=1,\qquad p\%=\frac{p}{100},\qquad x^{-1}=\frac1x

Factorial is implemented for nonnegative integers within the calculator's numeric range. Percent divides the preceding value by 100, and reciprocal requires a nonzero value.

Scientific Notation

a×10nwith1≤∣a∣<10a\times10^n\qquad\text{with}\qquad1\le |a|<10

The EXP key appends a base-10 exponent to the current number. For example, 6.02 EXP 23 represents 6.02 times 10 to the power of 23.

Precision and Display

The engine evaluates expressions as JavaScript numbers and the display keeps up to 12 significant digits. Answers with very large or very small magnitudes can appear in scientific notation.

Do not round each intermediate step. Retain the calculator result during the calculation and round only the final answer to the precision required by the problem.

References

These references support the calculation method, assumptions, or current program guidance.

Corrections and Review

Report an issue or error in the calculator using the Contact Us page.

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